I am reading "Multiple View Geometry" book, and there is the following line there: $$v = \lim_{\lambda\to\infty} x(\lambda) = \lim_{\lambda\to\infty}(a+\lambda Kd) = Kd,$$ where $x(\lambda) = PX(\lambda) = PA + \lambda PD = a + \lambda Kd$ ($a$ is the image of $A$), $D = (d^T,0)^T$ is a direction, and $P=K[I|0]$ is a projective camera.
It seems that the derivative is taken from the $\lim$, so the L'Hopitale's rule is used. But I do not understand how it can be applied since there is no division inside the limit. How is it derived?